基于低秩模型的海量分布式空间数据并行推理
Parallel inference for massive distributed spatial data using low-rank models
摘要：
由于数据的快速增长，大规模数据集的统计分析通常必须以分布式方式进行，因为存储在不同物理位置的多个数据集都与给定问题相关，或者仅仅是为了通过分治方案实现更快的（并行）计算。在这两种情况下，挑战在于获得有效的推理，而不需要在单个中央计算节点处理所有数据。我们发现，对于一类非常广泛使用的空间低秩模型，它可以被写为空间基函数的线性组合加上细尺度变化组件，并行空间推理和预测的大规模分布式数据可以进行准确，这意味着结果是相同的传统的，非分布的分析。我们的分布式算法的通信成本不依赖于数据点的数量。在将我们的结果扩展到时空的情况下，我们通过对三个不同的卫星传感器系统测量的总可降水量进行分布式时空粒子滤波推断来说明我们的方法。
英文摘要：
Due to rapid data growth, statistical analysis of massive datasets often has to be carried out in a distributed fashion, either because several datasets stored in separate physical locations are all relevant to a given problem, or simply to achieve faster (parallel) computation through a divide-and-conquer scheme. In both cases, the challenge is to obtain valid inference that does not require processing all data at a single central computing node. We show that for a very widely used class of spatial low-rank models, which can be written as a linear combination of spatial basis functions plus a fine-scale-variation component, parallel spatial inference and prediction for massive distributed data can be carried out exactly, meaning that the results are the same as for a traditional, non-distributed analysis. The communication cost of our distributed algorithms does not depend on the number of data points. After extending our results to the spatio-temporal case, we illustrate our methodology by carrying out distributed spatio-temporal particle filtering inference on total precipitable water measured by three different satellite sensor systems.
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